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A002106
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Number of transitive permutation groups of degree n.
(Formerly M1316 N0504)
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17
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1, 1, 2, 5, 5, 16, 7, 50, 34, 45, 8, 301, 9, 63, 104, 1954, 10, 983, 8, 1117, 164, 59, 7, 25000, 211, 96, 2392, 1854, 8, 5712, 12, 2801324, 162, 115, 407, 121279, 11, 76, 306, 315842, 10, 9491, 10, 2113, 10923, 56, 6
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OFFSET
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1,3
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COMMENTS
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It is conjectured that this is the number of Galois groups for irreducible polynomials of order n. (All such Galois groups are transitive.) - Charles R Greathouse IV, May 28 2014
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REFERENCES
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G. Butler and J. McKay, personal communication.
C. C. Sims, Computational methods in the study of permutation groups, pp. 169-183 of J. Leech, editor, Computational Problems in Abstract Algebra. Pergamon, Oxford, 1970.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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D. Holt, Enumerating subgroups of the symmetric group, in Computational Group Theory and the Theory of Groups, II, edited by L.-C. Kappe, A. Magidin and R. Morse. AMS Contemporary Mathematics book series, vol. 511, pp. 33-37. [Annotated copy]
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EXAMPLE
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a(3)=2: A_3 and S_3.
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PROG
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(GAP) a:=function(n)
return Length(AllTransitiveGroups(NrMovedPoints, n));
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CROSSREFS
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KEYWORD
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nonn,core,hard,more,nice,changed
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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